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Wittaler [7]
3 years ago
14

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and tes

t 13 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6​% rate of​ defects, what is the probability that this whole shipment will be​ accepted?
Mathematics
1 answer:
Pavel [41]3 years ago
6 0

Answer:

0.818

Step-by-step explanation:

Since the shipment has a ton of aspirin tablets, we can assume that we pick 13 of them <em>with</em> <em>reposition, </em>because the probability shoudn't change dramatically from the probability of picking without reposition if we do so.

We call D the amount of defective tablets. If we assume that we pick the tablets with reposition, then we obtain that D is a random variable of Binomial distribution with parameters 13 and 0.6 (the probability of picking a defective tablet).

We want D to be at most one. To calculate the probability of that event we add up the probability of D being equal to 0 and the probability of D being equal to one. Since D is binomial, we have

  • P(D = 0) = (1-0.06)^{13} = 0.447
  • P(D = 1) = {13 \choose 1} * 0.06^1 * (1-0.06)^{12} = 13*0.06*0.94^{12} = 0.371

We conclude that

P(D \leq 1) = P(D = 0) + P(D = 1) = 0.447+0.371 = 0.818

Hence, the shipment will be accepted with probability 0.818

<em>I hope this helps you!</em>

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aliina [53]

Answer:

System 1 : {3,0};  System 2 : {6,-2}

Step-by-step explanation:

2x + 3y = 6

-2x - y = -6

2y = 0

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-2x = -6

x = 3

system 2

2x + 3y = 6

2x + 2y = 8

y = -2

2x -4 = 8

2x = 12

x = 6

6 0
2 years ago
Help, I tried it, but I keep getting the wrong answers
Aneli [31]

Answer:

my answer would be that

x = 17.91cm

(i'm not sure about it either but it's worth a try) !!

Step-by-step explanation:

so first off, using the equation given,

" c² = a² + b² — 2ab cos C "

we substitute the values in as,

a = 16

b = 30

then for C is the angle given, which is 30°

so the equation is now,

c² = (16)² + (30)² — 2(16)(30) cos 30°

now, you solve the two squared numbers and the back equation, also known as " 2ab cos C " with your scientific calculator.

so it now equals to,

c² = 256 + 900 — 960(0.87)

c² = 320.8

at last, when you have " c² = 320.8 " ,

remember to square root the answer so you have a smaller value.

so,

c equals to

\sqrt{320.8}

your final answer for the x value will be 17.91

(i hope this helps!)

8 0
3 years ago
A squirrel ran 9 miles in 1 hour. Which expression can be used to determine its speed in miles per hour?
a_sh-v [17]

Answer:

9 mile/ 1 hour

Step-by-step explanation:

Because the squirrel ran 9 miles in 1 hour, so u have to divide 9 miles by 1 hour.

8 0
3 years ago
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Andru [333]

Answer:

0.25 ( I guess)

Step-by-step explanation:

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3 years ago
Which equation represents a parabola that opens upward, has a minimum at x = 3, and has a line of symmetry at x = 3?
densk [106]

Answer:

A.\ y = x^2 - 6x + 13 is the correct answer.

Step-by-step explanation:

We know that vertex equation of a parabola is given as:

y = a(x-h)^2+k

where (h,k) is the vertex of the parabola and

(x,y) are the coordinate of points on parabola.

As per the question statement:

The parabola opens upwards that means coefficient of x^{2} is positive.

Let a = +1

Minimum of parabola is at x = 3.

The vertex is at the minimum point of a parabola that opens upwards.

\therefore h = 3

Putting value of a and h in the equation:

y = 1(x-3)^2+k\\\Rightarrow y = (x-3)^2+k\\\Rightarrow y = x^2-6x+9+k

Formula used: (a-b)^2=a^{2} +b^{2} -2\times a \times b

Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.

Comparing y = x^2 - 6x + 13 and y = x^2-6x+9+k

13 = 9+k

k = 4

Please refer to the graph attached.

Hence, correct option is A.\ y = x^2 - 6x + 13

3 0
3 years ago
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